Dynamical models and tracking regret in online convex programming

Modern sensors are collecting data at unprecedented rates, often from
platforms with limited processing power and bandwidth for data
transmission. To cope with this data deluge, we must develop robust
methods for efficiently extracting information from large-scale
streaming data. Online optimization methods are often designed to have
a total accumulated loss comparable to that achievable by some
comparator, such as a batch algorithm with access to all the data and
infinite computational resources; the associated "regret" bounds scale
with the overall variation of the comparator sequence. However, in
practical scenarios ranging from motion imagery to network analysis,
the environment is nonstationary and comparator sequences with small
variation are quite weak, resulting in large losses. I will describe a
"dynamic mirror descent" method which addresses this challenge,
yielding low regret relative to highly variable comparator sequences
by both tracking the best dynamical model and forming predictions
based on that model. This concept is demonstrated empirically in the
context of sequential compressive observations of a dynamic scene and
tracking a dynamic social network.

Rebecca Willett is an associate professor in the Electrical and
Computer Engineering Department at Duke University. She completed her
PhD in Electrical and Computer Engineering at Rice University in 2005.
Prof. Willett received the National Science Foundation CAREER Award in
2007, is a member of the DARPA Computer Science Study Group, and
received an Air Force Office of Scientific Research Young Investigator
Program award in 2010. Prof. Willett has also held visiting researcher
positions at the Institute for Pure and Applied Mathematics at UCLA in
2004, the University of Wisconsin-Madison 2003-2005, the French
National Institute for Research in Computer Science and Control
(INRIA) in 2003, and the Applied Science Research and Development
Laboratory at GE Healthcare in 2002. Her research interests include
network and imaging science with applications in medical imaging,
wireless sensor networks, astronomy, and social networks. Additional
information, including publications and software, are available online
at http://www.ee.duke.edu/~willett/.